Find the coordinates of the point P that divides the directed line segment from A to B in the given ratio.
A(5,6), B(−5, −9); 3 to 2

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grujan50 grujan50 · Answer 1 · 2019-01-25T02:13:47+01:00

Answer:

P ( -1, -3)

Step-by-step explanation:

Given ratio is AP : PB = 3 : 2 = m : n and points A(5,6) B(-5,-9)

We will calculate coordinates of the point P which divides line segment AB

in the following way:

xp = (n · xa + m · xb) / (m+n) = (2 · 5 + 3 · (-5)) / (3+2) = (10-15) / 5 = -5/5 = -1

xp = -1

yp = (n · ya + m · yb) / (m+n) = (2 · 6 + 3 · (-9)) / (3+2) = (12-27) / 5 = -15/5 = -3

yp = -3

Point P( -1, -3)

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raphealnwobi raphealnwobi · Answer 2 · 2022-01-25T12:20:27+01:00

The coordinates of the point P that divides the directed line segment from A to B in the ratio 3:2 is (-1, -3).

If point P(x, y) divides line segment AB with end points at A(x₁, y₁) and B(x₂, y₂) in the ratio n:m, the coordinate of P is at:

[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1 \\ \\ y=\frac{n}{n+m}(y_2-y_1)+y_1 [/tex]

Given A(5,6), B(−5, −9); 3 to 2, hence:

The coordinates of the point P that divides the directed line segment from A to B in the ratio 3:2 is (-1, -3).

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